129:20 When leaving shul on Rosh Hashana, one should walk peacefully and pleasantly, happy and in good spirits, confident that Hashem has heard our prayers and our shofar blowing in mercy. One eats and drinks according to Hashem’s bounty (because, even though it is a day of judgment, it is also a holiday and the obligation to rejoice on yom tov still applies – Mishnah Brurah 597:1). We should not overeat. One should study Torah at the table and, after bentching, he should not sleep. Rather, one should go to shul in order to say Tehillim with the congregation until it is the time for mincha. If one is very tired, he is permitted to sleep a little before returning to shul. (The Ari permits one to sleep after midday – MB 583:9.)
129:21 After mincha on the first day of Rosh Hashana, we go to a river as an allusion to what the Midrash tells us regarding the binding of Isaac: When Abraham went to offer his son Isaac, the “accuser” turned himself into a river in order to delay them. Abraham went in the river up to his neck and called out, “Save me, Hashem, because the waters have come up to my soul” (Psalms 69:2). Another explanation for the custom to perform Tashlich at a river is that on Rosh Hashana we make Hashem king over us, and kings were typically annointed by a river.
Optimally, the river should be outside of the city and it should contain fish. This reminds us that, just as fish can be caught, so are we trapped in the snare of death and judgment. This realization should inspire us to repent. Still another explanation is that it serves as a sign that the ayin hara (“evil eye”) has no power over us just as it has no power over fish, plus we should be fruitful and multiply like fish. Some say that the reason is that fish do not have eyelids, with the result that their eyes are always open. So, too, should our eyes be awakened to watchfulness.
If there is no local river with fish in it, one goes to a diiferent river or another body of water and recites the verses starting “Who is a G-d like You…?” (Micah 7:18) that appear in machzor under the name “Tashlich.” We shake out the corners of our garments as a sign to throw away our sins and to investigate our deeds from this day forth so that we should be clean of any sins. If the first day of Rosh Hashana falls on a Shabbos, then we go to the river on the second day.